Numerical simulation of unsteady cavitating flows around a transient pitching hydrofoil

Abstract

The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. The effects of pitching rate on the subcavitating and cavitating response of the pitching hydrofoil are also investigated. In particular, we focus on the interactions between cavity inception, growth, and shedding and the vortex flow structures, and their impacts on the hydrofoil performance. The calculations are 2-D and performed by solving the incompressible, multiphase Unsteady Reynolds Averaged Navier Stokes (URANS) equations via the commercial CFD code CFX. The k-ω SST (Shear Stress Transport) turbulence model is used along with the transport equation-based cavitation models. The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density. The calculation results are validated with experiments conducted by Ducoin et al. (see Computational and experimental investigation of flow over a transient pitching hydrofoil, Eur J Mech/B Fluids, 2009, 28: 728–743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in various flow regimes including cavitating flow, Eur J Mech B/fluids, 2012, 36: 63–74). Results are shown for a NACA66 hydrofoil subject to slow (quasi static, $\dot \alpha = {{6^ \circ } \mathord{\left/ {\vphantom {{6^ \circ } s}} \right. \kern-\nulldelimiterspace} s}$, $\dot \alpha ^ * = 0.18$) and fast (dynamic, $\dot \alpha = {{63^ \circ } \mathord{\left/ {\vphantom {{63^ \circ } s}} \right. \kern-\nulldelimiterspace} s}$, $\dot \alpha ^ * = 1.89$) pitching motions from α = 0° to α = 15°. Both subcavitaing (σ=8.0) and cavitating (σ=3.0) flows are considered. For subcavitating flow (σ=8.0), low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall, and delay of stall is observed with increasing pitching velocity. For cavitating flow (σ=3.0), small leading edge cavities are observed with the slow pitching case, which significantly modified the vortex dynamics at high angles of attack, leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate. On the other hand, for the fast pitching case at σ=3.0, large-scale sheet/cloud cavitation is observed, the cavity behavior is unsteady and has a strong impact on the hydrodynamic response, which leads to high amplitude fluctuations of the hydrodynamic coefficients, as well as significant changes in the stall and post-stall behavior. The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region, which significantly modifies the cavity lengths and shedding frequencies, particularly for the fast pitching case. In general, compared with the experimental visualizations, the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.